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Can Ice Tables Be Used for Pressure?

Published in Chemical Equilibrium 4 mins read

Yes, ICE tables can be used for pressure calculations, particularly when dealing with equilibrium problems involving gases.

Understanding ICE Tables and Pressure

An ICE table (Initial, Change, Equilibrium) is a tool used to calculate the equilibrium concentrations or partial pressures of reactants and products in a reversible reaction. When dealing with gaseous reactions, you can adapt the ICE table to work with partial pressures instead of molar concentrations. This is especially useful when the equilibrium constant is expressed in terms of partial pressures (Kp) rather than molar concentrations (Kc).

How to Use ICE Tables for Pressure

Here's how you can use ICE tables with pressure:

  1. Set up the ICE table: Create a table with rows labeled Initial (I), Change (C), and Equilibrium (E). The columns will represent each gaseous reactant and product in the balanced chemical equation.

  2. Initial Partial Pressures (I): Fill in the initial partial pressures of each gas. If a gas is not initially present, its initial partial pressure is zero.

  3. Change in Partial Pressures (C): Determine the change in partial pressure for each gas as the reaction proceeds towards equilibrium. This will be based on the stoichiometry of the balanced chemical equation. For example, if the coefficient of a reactant is 2, and it's being consumed, the change in its partial pressure might be -2x, where 'x' is a variable representing the change in pressure. Products will have a positive change in partial pressure.

  4. Equilibrium Partial Pressures (E): Calculate the equilibrium partial pressures by adding the change to the initial partial pressures (E = I + C).

  5. Kp Expression: Write the expression for the equilibrium constant Kp in terms of the partial pressures of the products and reactants at equilibrium.

  6. Solve for x: Substitute the equilibrium partial pressures (in terms of 'x') into the Kp expression and solve for 'x'.

  7. Calculate Equilibrium Partial Pressures: Once you've found the value of 'x', substitute it back into the expressions for the equilibrium partial pressures to find the numerical values.

Example

Consider the following gaseous reaction:

N2(g) + 3H2(g) ⇌ 2NH3(g)

Suppose the initial partial pressures are P(N2) = 2 atm, P(H2) = 5 atm, and P(NH3) = 0 atm, and Kp = 0.05.

N2 (g) 3H2 (g) 2NH3 (g)
Initial (I) 2 5 0
Change (C) -x -3x +2x
Equilibrium (E) 2-x 5-3x 2x

Kp = P(NH3)2 / [P(N2) * P(H2)3]

  1. 05 = (2x)2 / [(2-x) * (5-3x)3]

Solving for 'x' (which may require approximations or numerical methods) will allow you to determine the equilibrium partial pressures of each gas.

Key Considerations

  • Units: Ensure that all partial pressures are in the same units (e.g., atm, kPa).
  • Kp vs. Kc: Remember that Kp and Kc are related but not identical. You can convert between them using the equation Kp = Kc(RT)Δn, where Δn is the change in the number of moles of gas in the reaction.
  • Assumptions: In some cases, you can simplify the calculation by assuming that 'x' is small compared to the initial pressures. This is valid if Kp is small. However, you should always check the validity of this assumption.

By using ICE tables with partial pressures and the Kp expression, you can effectively solve equilibrium problems involving gaseous reactions.

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